Solve 2p(p-3m)-(p-3m)^2=

$$2 p ( p - 3 m ) - ( p - 3 m ) ^ { 2 } =$$

Evaluate

$$p^{2}-9m^{2}$$

Solution Steps

Use the distributive property to multiply 2p by p-3m.

$$2p^{2}-6pm-\left(p-3m\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(p-3m\right)^{2}.

$$2p^{2}-6pm-\left(p^{2}-6pm+9m^{2}\right)$$

To find the opposite of p^{2}-6pm+9m^{2}, find the opposite of each term.

$$2p^{2}-6pm-p^{2}+6pm-9m^{2}$$

Combine 2p^{2} and -p^{2} to get p^{2}.

$$p^{2}-6pm+6pm-9m^{2}$$

Combine -6pm and 6pm to get 0.

$$p^{2}-9m^{2}$$

Expand

$$p^{2}-9m^{2}$$

Solution Steps

Use the distributive property to multiply 2p by p-3m.

$$2p^{2}-6pm-\left(p-3m\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(p-3m\right)^{2}.

$$2p^{2}-6pm-\left(p^{2}-6pm+9m^{2}\right)$$

To find the opposite of p^{2}-6pm+9m^{2}, find the opposite of each term.

$$2p^{2}-6pm-p^{2}+6pm-9m^{2}$$

Combine 2p^{2} and -p^{2} to get p^{2}.

$$p^{2}-6pm+6pm-9m^{2}$$

Combine -6pm and 6pm to get 0.

$$p^{2}-9m^{2}$$